I'm not sure what card to get either. Finding mid range graphics solutions that fit in a small form factor desktop, don't overheat, or have a screaming fan can be an exercise in frustration. Finding new components that are compatible with older systems can also add challenges. Let's begin...

The dc7800 Hardware Reference Guide for this system available on HP's website describes...
1. ... the motherboard interfaces available for expansion cards and discusses variants. The basic system has one PCI slot, two PCI Express slots, and one PCI Express x16 slot. All are low-profile, also called half-height, form factor interfaces. For optimal graphic performance, the video card should be placed in the PCI Express x16 slot, necessitating a video card with this interface. This system can also be configured with a PCI riser card that allows full height cards but rotated 90 degrees to the usual orientation. This is useful for being able to use full height cards, but in this case it would limit the cards to a PCI interface which would be detrimental performance-wise for gaming and also block the PCI Express slots. If your system has a PCI riser it can be removed to gain access to the PCI Express x16 slot.

2. ... available space. The guide states 17.46 cm (6.875 inches) is available for card length. Also, the PCI Express x16 slot sits between two x1 slots which would allow for a double slot width card, but would block one of the x1 slots.

3. ... power supply. The dc7800 has a 240 watt power supply to be cognizant of when selecting video cards. The available power margin should be calculated based on the other components in the system and either select a card that fits within the margin or upgrade the power supply. Also the hardware guide does not indicate if the power supply has 6-pin video card power connectors used with newer cards which could require a power adapter if they are lacking.

4. ... thermal management. I suggest giving preference to lower power or fanless cards, but that have the performance you need, to help mitigate overheating. Easier said than done.

Armed with the parameters above and using a shopping site like Newegg.com that has the ability to filter cards by form factor, interface, length, GPU and other factors will ease narrowing down the field of possible card candidates. Knowing the recommended card requirements of the games you want to play is also helpful for excluding cards with earlier GPUs that don't have the performance necessary for your current games or a performance margin to be able to handle future games. Relative card performance can be compared with Video Card (GPU) Benchmark Charts.

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